These are some things I learned from re-learning to paint minis about 15 years ago.
Start small - I've seen people basically say, "I'm just starting out painting, so I'm getting the full collection of (whatever model paint line they think is awesome) plus a variety of W&N Series 7 brushes, a pallete, a new painting desk, a custom painting lamp," etc. etc.
I wouldn't do that. Honestly, just grab either:
a) A minis-specific Learn-to-Paint Kit
b) A small variety (10-12 bottles) of craft paints, a couple of reasonably small craft brushes, a couple emery boards to file minis, and a bottle of automotive primer.
That's all you need to start. Start with just-good-enough stuff and you'll be fine. Buying the top-end stuff right away is a waste. For one thing, you don't know if you'll like painting, so start cheap. Second, you have no experience of paints and materials so you're buying from reputation not from actual experience knowing you need the upgrade. Third, you won't be so much better off with the better tools because you don't have the experience to use them. It works out to be, basically, a waste of money. Even more so if you buy them and don't really know how to control the amount of paint, keep the brushes intact, etc. Practice on the cheaper stuff. Basically, learn to drive on a cheap beater, not on a Ferrari. Then upgrade the bits little by little - you'll know what gear to upgrade, what paint sucks (and what paint doesn't), what brushes sizes you find comfortable.
Not only that, you'll have a collection of beater brushes and large-area paints and such to use when you just need to get paint onto something - terrain, bases, big minis taking washes, and the like.
Paint Brush Cleaner - This you want to start at the top-end with. Get a small pot of The Master's Brush Cleaner and Restorer and use it from day one. Never leave paint to dry on your brushes and don't trust they are clean until they wash with no color on The Master's. Get a 2.5 oz container. I'm still using the same 2.5 oz container I bought about 10+ years ago and I think I have more than half left.
And don't get paint up to the ferrule.
Don't Strip and Repaint
Pick a few minis to start with. Clean them, file them, prime them, paint them. Then seal them and you are done. Don't strip them of paint and re-start. Seriously, don't. Keep them around as a reminder of how you started. Also, keep them around so you can take a look at your new paint jobs side by side with your earlier ones and compare technique.
If you get into the habit of ripping up your canvases and starting over, you'll end up with nothing but unpainted minis and frustration.
Save stripping and repainting for when disaster really strikes (oops, dropped the mini onto a dusty bunny while it was wet) or you have a one-of-a-kind mini and really need it just right. 95%+ of the time, this won't happen.
Think of all the not-so-good minis as practice. Don't scrap your practice or you might miss out on the improvement it brings.
Picking the minis
As I've said before, paint reveals, not conceals. My best advice is to pick minis that are neither too detailed (ahem), or not detailed enough (think plastic army men here.)
Too detailed? You'll be fiddling forever with your early minis. ("Now, only four more pouches to go and then I can start painting the first of his two packs.")
Not detailed enough? You end up frustrated because paint reveals the lack of accurate detail on the figure. ("Why does his belt only show up on the front? Where do these pants end and the legs begin? Is that a bag or a lump? Why does his mail armor just sort of stop halfway up the mini?")
It's up to you if you want to start an army - so you can paint a lot of the same kind of guys and get good at it - or do individuals - so you can move on after you try something.
Learn New Techniques ASAP
One thing I didn't do. I quickly got into a painting rut. I improved the rut (leveled the floor, smoothed the sides) but stayed in a rut. It took a long time to get me to branch out. Try to add new paint techniques to your repertoire from day one. I'd suggest going as far as finding a video or text instruction, buying the same mini they're using to demonstrate, and copying the technique. Then you can branch out and try it on other minis with other colors.
If you're not a video or text learner, I understand - I'm someone who needs you to show me how. Find someone who paints and ask for lessons or if you can paint side-by-side for a while and copy what they do. Don't stagnate like I did. Experiment and learn.
Most of all, though, enjoy the process. Enjoy the learning, the errors, the practice, the figure prep, the rushing outside on the nice days to get things primed and ready.
If you like painted figures but don't like painting, buy painted figures. As much as I love having well-painted figures on the table, I'm sort of like Jackie Chan - it's not enough to say, "Check that stunt out!" I want to say, "I did that." I enjoy the actual process, I love looking at a finished figure and seeing what I made out of some pots of paint, a brush, and a bare metal or plastic figure. You need to like the process as much as the finished product or it's worth it just to skip to the final product.